Human motor learning is useful if it generalizes beyond the trained task. Here, we introduce a new idea about how human visuomotor learning generalizes. We show that learned reaching movements generalize around where a person intends to move (i.e., aiming direction) as opposed to where they actually move. We used a visual rotation paradigm that allowed us to disentangle whether generalization is centered on where people aim to move, where they actually move, or where visual feedback indicates they moved. Participants reached to a visual target with their arm occluded from view. The cursor feedback was rotated relative to the position of their unseen hand to induce learning. Participants verbally reported their aiming direction, reached, and then were shown the outcome. We periodically introduced single catch trials with no feedback to measure learning. Results showed that learning was maximal at the participants' aiming location, and not at the actual hand position or where the cursor was displayed. This demonstrates that visuomotor learning generalizes around where we intend to move rather than where we actually move, and thus introduces a new role for cognitive processes beyond simply reducing movement error.